Prosthetic heart valves having a conical shaped base valve structure formed from collagenous mammalian tissue. The base valve structure includes a plurality of elongated ribbon members that are positioned proximate each other in a joined relationship, wherein the elongated ribbon members are positioned adjacent each other and form a plurality of fluid flow modulating regions that open when fluid into and through the base valve structure exhibits a positive pressure relative to the exterior pressure, i.e., a positive pressure differential, wherein the fluid is allowed to be transmitted out of the base valve structure, and transition to a closed configuration when the pressure differential between the interior valve pressure and exterior pressure reduces, wherein the fluid is restricted from flowing out of the base valve structure.